Algebra Calculator and Steps

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Linear Equation Solver (ax + b = c)

Result:

Enter values and click 'Solve Equation' to see the result.

Steps:

function calculateAlgebra() { var coeffA = parseFloat(document.getElementById("coeffA").value); var constB = parseFloat(document.getElementById("constB").value); var constC = parseFloat(document.getElementById("constC").value); var resultX = document.getElementById("resultX"); var stepList = document.getElementById("stepList"); stepList.innerHTML = ""; // Clear previous steps if (isNaN(coeffA) || isNaN(constB) || isNaN(constC)) { resultX.innerHTML = "Please enter valid numbers for all fields."; return; } var steps = []; steps.push("Starting equation: " + coeffA + "x + " + constB + " = " + constC); if (coeffA === 0) { if (constB === constC) { resultX.innerHTML = "Solution: Infinite solutions (any real number for x)"; steps.push("Since the coefficient of x (a) is 0, the equation becomes " + constB + " = " + constC + "."); steps.push("As " + constB + " equals " + constC + ", this statement is always true, meaning x can be any real number."); } else { resultX.innerHTML = "Solution: No solution"; steps.push("Since the coefficient of x (a) is 0, the equation becomes " + constB + " = " + constC + "."); steps.push("As " + constB + " does not equal " + constC + ", this statement is false, meaning there is no value for x that satisfies the equation."); } } else { // Step 1: Isolate the term with x var cMinusB = constC – constB; steps.push("Subtract " + constB + " from both sides of the equation:"); steps.push(coeffA + "x = " + constC + " – " + constB); steps.push(coeffA + "x = " + cMinusB); // Step 2: Solve for x var xValue = cMinusB / coeffA; steps.push("Divide both sides by " + coeffA + ":"); steps.push("x = " + cMinusB + " / " + coeffA); steps.push("x = " + xValue.toFixed(4)); // Display with 4 decimal places resultX.innerHTML = "Solution for x: " + xValue.toFixed(4) + ""; } // Display steps for (var i = 0; i < steps.length; i++) { var listItem = document.createElement("li"); listItem.textContent = steps[i]; stepList.appendChild(listItem); } }

Understanding Linear Equations and How to Solve Them

Algebra is a fundamental branch of mathematics that uses letters (variables) to represent numbers and quantities in equations. One of the most common types of equations you'll encounter is the linear equation. A linear equation is an algebraic equation in which each term has an exponent of 1, and when graphed, it forms a straight line. The simplest form of a linear equation with one variable is often expressed as ax + b = c.

What is a Linear Equation?

In the equation ax + b = c:

  • x is the variable, the unknown value we want to find.
  • a is the coefficient of x. It's the number that multiplies x.
  • b is a constant term on the left side of the equation.
  • c is a constant term on the right side of the equation.

The goal when solving a linear equation is to isolate the variable x on one side of the equation, typically the left side, to find its value.

Steps to Solve ax + b = c

Solving a linear equation involves applying inverse operations to both sides of the equation to maintain balance. Here's a breakdown of the general steps:

  1. Isolate the term with the variable (ax):

    To get the ax term by itself, you need to eliminate the constant term b from the left side. You do this by performing the inverse operation of what's being done to b. If b is being added, you subtract b from both sides of the equation. If b is being subtracted, you add b to both sides.

    So, ax + b = c becomes ax = c - b.

  2. Solve for the variable (x):

    Now that you have ax on one side and a constant on the other, you need to get x by itself. Since a is multiplying x, the inverse operation is division. You divide both sides of the equation by a.

    So, ax = c - b becomes x = (c - b) / a.

Special Cases:

  • If a = 0:

    If the coefficient of x is zero, the equation simplifies to 0x + b = c, or simply b = c.

    • If b = c (e.g., 5 = 5), then the equation is true for any value of x. This means there are infinite solutions.
    • If b ≠ c (e.g., 5 = 7), then the equation is false. This means there is no solution.

Example Using the Calculator:

Let's solve the equation 3x + 5 = 14 using the calculator above.

  1. Input 3 for "Coefficient of x (a)".
  2. Input 5 for "Constant Term (b)".
  3. Input 14 for "Right Side Constant (c)".
  4. Click "Solve Equation".

The calculator will show the following steps:

  • Starting equation: 3x + 5 = 14
  • Subtract 5 from both sides: 3x = 14 - 5
  • 3x = 9
  • Divide both sides by 3: x = 9 / 3
  • x = 3

The solution for x is 3.

This calculator provides a quick way to solve simple linear equations and understand the step-by-step process involved, reinforcing your algebraic skills.

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